Following a growing concern among investors about the quality of hedge fund index return data, and given the lack of capacity and transparency specific to that industry, this paper questions from an academic perspective whether it is feasible or not to design hedge fund benchmarks satisfying all defining properties for a good index.

In particular, in an attempt to test whether achieving investability necessarily comes at the cost of representativity, as sometimes claimed by hedge fund index providers, we borrow from the asset pricing literature the concept of factor replicating portfolios and apply it to the benchmarking of hedge fund style returns. Our results suggest that it is actually possible to construct representative indices based on a limited number of funds, except perhaps in the case of Equity Market Neutral strategies, provided that i) these funds are suitably selected and ii) an optimal portfolio is designed with the objective of replicating the common trend in hedge fund returns for a given strategy. A wide range of tests are performed that show that high correlation of the factor replicating portfolios with the common factor of returns for each strategy is remarkably robustness with respect to modifying the number of funds in the replicating portfolio, choosing less correlated funds, changing the frequency of rebalancing, using a static selection of funds or imposing constraints on weights.

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